How do I cut a flap using edges or vertices
This can be done using the Rip tool. Go into edit mode, select and edge or a selection of edges (or a group of vertices):



Now press V. You will now get something like this:



For your specific instance do not select the shown edges.



Every edge is made from two vertices, one on each end. When you rip them, those vertices separate from the mesh, and a new edge is created. However the vertices at the end connect to the mesh still. In your example, pressing V would make there be a single vertex connecting the two parts, instead of two edges. Use the suggested selection to get the desire result.